Cut it twice, and there are at most 1+ 1+2=4 pieces.

Cut it three times, and there are at most 1+ 1+2=3=7 pieces.

Cut four knives, and the maximum is1+1+2 = 3+4 =11.

Cut five knives, at most1+1+2+3+4+5 =16.

Cut six times, and there are at most 1+ 1+2+3+4+5+6=22 pieces.

Cut 7 knives, at most1+1+2+3+4+5+6+7 = 29 pieces.

. . . . . .

Cut N knives, at most 1+ 1+2+3+...+n = (n? +n+2)/2